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arXiv · 1311.7403

Remarks on Privileged Words

Michael Forsyth·Amlesh Jayakumar·Jeffrey Shallit
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Abstract

We discuss the notion of privileged word, recently introduced by Peltomaki. A word w is privileged if it is of length <=1, or has a privileged border that occurs exactly twice in w. We prove the following results: (1) if w^k is privileged for some k >=1, then w^j is privileged for all j >= 0; (2) the language of privileged words is neither regular nor context-free; (3) there is a linear-time algorithm to check if a given word is privileged; and (4) there are at least 2^{n-5}/n^2 privileged binary words of length n.

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Michael Forsyth, Amlesh Jayakumar, Jeffrey Shallit. 2013-11-28. Remarks on Privileged Words. https://arxiv.org/abs/1311.7403

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